arXiv subjects

Shigekazu Nakagawa

Publications and source records attributed to Shigekazu Nakagawa.

2 recordsLinked to original sources

arXiv2021

Approximation to probability density functions in sampling distributions based on Fourier cosine series

We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the distribution of the sum of uniformly distributed random variables, and the distribution of sample skewness drawn from a normal population. The probability density function of the first example can be explicitly expressed, but that of the second example has no explicit expression.

math.ST↗

arXiv2012

A measure of skewness for testing departures from normality

We propose a new skewness test statistic for normality based on the Pearson measure of skewness. We obtain asymptotic first four moments of the null distribution for this statistic by using a computer algebra system and its normalizing transformation based on the Johnson $S_{U}$ system. Finally the performance of the proposed statistic is shown by comparing the powers of several skewness test statistics against some alternative hypotheses.

stat.CO↗